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p256 = 2^256 - 2^224 + 2^192 + 2^96 - 1
F = GF(p256)
a = F(-3)
b = F(41058363725152142129326129780047268409114441015993725554835256314039467401291)
E = EllipticCurve([a, b])
B = E(0x6b17d1f2e12c4247f8bce6e563a440f277037d812deb33a0f4a13945d898c296, 0x4fe342e2fe1a7f9b8ee7eb4a7c0f9e162bce33576b315ececbb6406837bf51f5)
def orzero(x):
if not x:
return "0"
return x
def hex4(x):
x = int(x)
M = int(2^64-1)
return hex((x>>(3*64))&M) +', '+ hex((x>>(2*64))&M) +', '+ hex((x>>64)&M) +', '+ hex(x&M)
R = 2^256
testcount = [0]
def print_test(J, Z1, A):
Z1 = F(Z1)
print ("{")
print ("uint64_t out[12] = {0};")
if not J.is_zero():
X1, Y1 = J.xy()
X1 = X1 * Z1^2
Y1 = Y1 * Z1^3
else:
X1 = F(32421522)
Y1 = F(-451234651326)
Z1 = 0
if not A.is_zero():
X2, Y2 = A.xy()
else:
X2 = 0
Y2 = 0
print ("uint64_t J[12] = {" + hex4(R*X1) +", " + hex4(R*Y1) + ", " + hex4(R*Z1) + "};")
print ("uint64_t A[8] = {" + hex4(R*X2) +", " + hex4(R*Y2) + "};")
P = J+A
if not P.is_zero():
X3, Y3 = P.xy()
if not J.is_zero() and not A.is_zero():
print ("// both nz")
Z3 = Z1 * (Z1^2*X2 - X1)
elif not J.is_zero():
print ("// J nz")
Z3 = Z1
else:
print ("// maybe A nz, maybe neither")
Z3 = F(1)
X3 = X3 * Z3^2
Y3 = Y3 * Z3^3
else:
X3 = X1
Y3 = Y1
Z3 = 0
print ("p256_jacobian_add_affine(out, J, A);")
print ("uint64_t ref[12] = {" + hex4(R*X3) +", " + hex4(R*Y3) + ", " + hex4(R*Z3) + "};")
testcount[0] = testcount[0] + 1
print ("if (memcmp(out, ref, sizeof(uint64_t)*12)) return %d;"%testcount[0])
print ("}")
P = E(0, sqrt(b))
print ("""
#include <string.h>
#include <stdint.h>
#include "p256.h"
int main() {
""")
print_test(B,1, P)
print_test(B,1, -P)
print_test(B,2, P)
print_test(B,2, -P)
print_test(P,2, P)
print_test(P,-1, P)
print_test(-P,1, B)
print_test(-P,-1, B)
print_test(B-B,0, B)
print_test(P,1, B-B)
print_test(P,-1, B-B)
print_test(B,1, B-B)
import random
random.seed(314)
for i in range(200):
print_test(random.randint(0,100)*B,random.randint(1,100)^random.randint(0,10), random.randint(0,100)*P)
print("""
return 0;
}""")
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